You are a consultant to a firm evaluating an expansion of its current business.

Question

You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are as follows: 0100 1-1018 On the basis of the behavior of the firm's stock, you believe that the beta of the firm is 1.31. Assuming that the rate of return available on risk-free investments is 4% and that the expected rate of r eturn on the market portfolio is 14%, what is the net present value of the millions of doili amount should be Indicated by a minus sign. Do not round Intermediate calculations. Enter your answer in ars rounded to 2 decimal places.)

Explanation / Answer

First, compute the expected return using CAPM -

ER = Rf + Beta x (Rm - Rf)

where, ER = expected return, Rf = risk free rate, Rm = return of market

ER = 4% + 1.31 x (14% - 4%) = 17.1%

We use this rate to compute the NPV.

NPV = (-)Initial Investment + Annual Cash Inflows x PVFA (rate, period)

or, NPV = (-)100 million +18 million x PVFA (17.1%, 10)

or, NPV = (-)100 million + 18 million x 4.64170984733 = (-)$16.449222749 or (-)$16.45

Note : Present value factor annuity (PVFA) is the sum of present value factors (PVF) for years 1 to 10. PVF is computed as 1 / (1 + r)t where t is the year for which it is computed. Like for year 1 - 1/ (1+0.171)1 and year 2 - 1/ (1+ 0.171)2 and so on. Add these till year 10 and you will get the PVFA.

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